Meiosis is the process of cell division involved in the production of the gametes (reproductive cells), creating cells with half of the amount of chromosomes than the rest of the cells of the body so they can merge in pairs (one from each parent) and create a new cell with the same amount of chromosomes as the rest of the cells. Meiosis is divided in two parts: Meiosis I and Meiosis II.
Before Meiosis I, the process starts with the Interphase, divided in three parts, in which the cell grows (G1), duplicates all of its chromosomes (S) and prepares for division (G2).
Then, Meiosis I starts with Prophase I. The chromosomes start to condense, pairing up to be organized in pairs of homologue chromosomes, matching up at correspondig positions.
The next fase is Metaphase I, in which the spindle is capturing the chromosomes and moving them to the center of the cell (metaphase plate). At this point of meioses, the homologue pairs are going together. They're are not divided into two separate chromosomes, they flow to the center of the cell in pairs.
In Anaphase I, the next fase, the homologues are pulled to opposite sides of the cell, separating the homologues but, still, the sister chromatides remain together forming the chromosomes.
In Telophase I, the end of Meiosis I, the chromosomes get to the opposite sides of the cell and cytokinesis occur (the cell is splited in two, forming two daughter cells).
Those daughter cells now will go through Meiosis II, but without copying their DNA. Those cells are haploids, meaning that they have only one chromosome from each homologue pair.
It starts with Prophase II, where the chromosomes condense and the spindle forms between centrosomes that are moving apart. The microtubules start capturing chromosomes. The difference from Meiosis I is that now each chromosome is captured by microtubules from opposite sides, because in Meiosis II the sister chromatids will be separated.
During Metaphase II the chromosomes line up individually (not in pairs, like happened during Meiosis I) along the metaphase plate, and during Anaphase II the sister chromatids are separated, being pulled to opposite poles of the cell.
The last phase is Telophase II, in which the chromosomes decondense and cytokinesis splits each cell in two, forming four haploid cells with just one chromatid in each chromosome.